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Re: Possible semantic bugs concerning domain and range

From: Jos De_Roo <jos.deroo.jd@belgium.agfa.com>
Date: Thu, 17 Oct 2002 00:11:04 +0200
To: Ian Horrocks <horrocks@cs.man.ac.uk>
Cc: Dan Connolly <connolly@w3.org>, Pat Hayes <phayes@ai.uwf.edu>, www-webont-wg@w3.org
Message-ID: <OF324356F0.D35200F8-ONC1256C54.0079A80D-C1256C54.0079DF00@agfa.be>


On October 16, Ian Horrocks writes:
>
> On October 16, Dan Connolly writes:
> >
> > On Wed, 2002-10-16 at 13:00, Ian Horrocks wrote:
> > > On October 16, Dan Connolly writes:
> > > >
> > > > On Tue, 2002-10-15 at 16:47, Jos De_Roo wrote:
> > > > >
> > > > > >> >>  Range(P, A) -> (forall x,y P(x,y) -> A(y) )
> > > > > >> >>
> > > > > >> >>  You want
> > > > > >> >>
> > > > > >> >>  Range(P,A) <-> (forall x,y P(x,y) -> A(y) )
> > > > > >> >>
> > > > > >> >>  They are about equally clear and intuitive; but the latter
rules out
> > > > > >> >>  some possibilities which the former permits. I believe
that all the
> > > > > >> >>  'intuitive' entailments that people want in fact hold in
both these
> > > > > >> >>  cases; and that the former is therefore to be preferred.
> > > > > >> >
> > > > > >> >I am agnostic about which of these is to be preferred - as a
humble
> > > > > >> >engineer, all I need to know is which one it is so that I
have a clear
> > > > > >> >spec to which I can build my systems.
> > > > > >
> > > > > >I'm kinda agnostic too... I was leaning toward the IF, rather
> > > > > >than the IFF...
> > > > >
> > > > > I'm not agnostic at all...
> > > > > i.e. I can't see how to write
> > > > >   (forall x,y P(x,y) -> A(y)) -> Range(P,A)
> > > > > in Horn-clauses or in Datalog
> > > > > (although I like nested implications
> > > > > in propositional proof arguments)
> > > >
> > > > Oohh; that's quite compelling... currently, you can
> > > > implement a complete RDFS reasoner with a
> > > > horn/datalog reasoner. If we changed range to IFF,
> > > > it's not clear that this property would hold.
> > > >
> > > > Likewise for subClassOf.
> > >
> > > If you use a direct encoding such as the one Benjamin and I have been
> > > suggesting (i.e., classes as unary predicates, properties as binary
> > > predicates),
> >
> > I don't see how that's relevant; if a test for C(i) -> D(i)
> > would work, then so would a test for
> >        holds(rdf:type, C, i) -> holds(rdf:type, D, i)
>
> Not unless you axiomatised the interaction between type and
> subClassOf. The whole point of the direct encoding is that subClassOf
> corresponds to implication, and you can let the logical machinery do
> the work for you - which is what it is designed for.

direct encoding can indeed be quite useful/performant
(we tend to use it for variable predicates)
so is it right that you add
  not(forall ?x C(?x) -> E(?x))
or in other words
  forsome i  C(i) & not(E(i)
but you also have E(i)
and so you have proven by contradiction ?

> E.g., if my Ontology says that C is a subClassOf D and that D is a
> subClassOf E, I add the rules C(?x) -> D(?x) and D(?x) -> E(?x) to my
> rule base. Now to check if C is a subClassOf E I can just add the fact
> C(i) to my rule base and check if E(i) is entailed by the rule
> base. In contrast, if I have the rules holds(rdf:subClassOf,C,D) and
> holds(rdf:subClassOf,D,E), then adding holds(rdf:type,C,i) would not
> entail holds(rdf:type,E,i) unless I add rule(s) that axiomatise the
> relationship between type and subClassOf.

I think there is some balance to be found between
direct encoding and axiomatization

> >
> > > then you can check if subClassOf(C,D) holds simply by
> > > inventing a new individual i and checking if C(i) -> D(i) holds.
> >
> > But in any case, how can I encode that as a horn clause?
> >
> >        subClassOf(C, D) :- ... what to put here? ...
>
> See above: I don't do this at all, I just check if C(x) entails D(x).
>
> Ian
>
> >
> >
> > > Similarly for Range(P,A), you can invent two new individuals i1 and
i2
> > > and check if P(i1,i2) -> A(i2) holds.
> > >
> > > Ian
> >
> > --
> > Dan Connolly, W3C http://www.w3.org/People/Connolly/
> >

-- ,
Jos De Roo, AGFA http://www.agfa.com/w3c/jdroo/
Received on Wednesday, 16 October 2002 18:11:41 GMT

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